Question

The following table gives the percentage, P, of households with a television set that also bave a VCR. (Unlike the data in your textbook this data is ficticious)

Year 1976 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991
% having VCR 0.2 0.4 0.8 1.4 2.9 5.4 9.5 16.7 25.4 37.9 46.5 53.8 56.7 60.5
a). During what year does to the point of "diminishing returns" (i.e., the inflection point) appear to take place?

Answer 1

The inflection point, or the point of diminishing returns, for the percentage of households with a television set that also have a VCR, appears to occur around the year 1989, where the rate of increase begins to slow down.

Step-by-step explanation:

The question asks to identify the year when the "diminishing returns" or the inflection point appears to take place based on the given percentage of households with televisions that also have a VCR for a range of years. The inflection point is when the rate of increase in the percentage of households with VCRs begins to slow down after a period of acceleration. To find this, one would look at the given data for a year where the percentage increase starts to decline from one year to the next.

From the provided data, we see a consistently increasing percentage until 1989 when the rate of increase starts to slow:

• 1987 to 1988 saw an increase of 8.6 (from 37.9% to 46.5%),
• but from 1988 to 1989 the increase was 7.3 (from 46.5% to 53.8%).

Thus, the inflection point appears to occur around the year 1989.